Spin-textures of medium-body boson systems with trapped spin-f cold atoms

The spin-textures of bound medium-body systems with spin-[Formula: see text] atoms ([Formula: see text]) have been studied. The Hamiltonian is assumed to be dominated by the two-body interaction favoring parallel spins. The system with particle number [Formula: see text] and [Formula: see text] is first chosen, and the Hamiltonian is exactly diagonalized by using Fock-states as basis-states, thereby all the eigenenergies and eigenstates are obtained and a detailed analysis is made. Then the cases with [Formula: see text] and [Formula: see text] are further studied. Since the total spin S is conserved, the eigenstates having the same S form an S-group. Let the lowest (highest) energy state of an S-group be called a bottom-state (top-state). We found that all the bottom-states are bipartite product states with constituent states describing fully polarized subsystems containing [Formula: see text] and [Formula: see text] ([Formula: see text]) particles, respectively. For two bottom-states different in [Formula: see text], the one with a larger [Formula: see text] is higher. For two having the same [Formula: see text], the one with a smaller S is higher. Whereas all the top-states are found to be essentially a product state of the pairs, in each pair the two spins are coupled to [Formula: see text] if the strength of the [Formula: see text]-channel is more repulsive than the others. For the states belonging to an S-group, the higher one would contain more pieces. As the energy goes up, larger pieces (those containing more than two particles) will disappear.